Catalytic effect of graphene on the inversion of corannulene using a continuum approach with the Lennard-Jones potential.

The catalytic effect of graphene on the corannulene bowl-to-bowl inversion is confirmed in this paper using a pair-wise dispersion interaction model. In particular, a continuum approach together with the Lennard-Jones potential are adopted to determine the interaction energy between corannulene and graphene. These results are consistent with previous quantum chemical studies, which showed that a graphene sheet reduces the barrier height for the bowl-to-bowl inversion in corannulene.

Variational model for a rippled graphene sheet.

The calculus of variations is utilised to study the behaviour of a rippled graphene sheet supported on a metal substrate. We propose a model that is underpinned by two key parameters, the bending rigidity of graphene , and the van der Waals interaction strength . Three cases are considered, each of which addresses a specific configuration of a rippled graphene sheet located on a flat substrate.

Carbon Nanocones with Curvature Effects Close to the Vertex.

The conventional rolled-up model for carbon nanocones assumes that the cone is constructed from a rolled-up graphene sheet joined seamlessly, which predicts five distinct vertex angles. This model completely ignores any effects due to the changing curvature, and all bond lengths and bond angles are assumed to be those for the planar graphene sheet. Clearly, curvature effects will become more important closest to the cone vertex, and especially so for the cones with the smaller apex angles.

Conformation of graphene folding around single-walled carbon nanotubes.

The low bending rigidity of graphene facilitates the formation of folds into the structure. This curvature change affects the reactivity and electron transport of the sheet. One novel extension of this is the intercalation of small molecules into these folds.

Energy behaviour for DNA translocation through graphene nanopores.

Nanoparticles have considerable promise for many applications in electronics, energy storage, bioscience and biotechnologies. Here we use applied mathematical modelling to exploit the basic principles of mechanics and the 6-12 Lennard-Jones potential function together with the continuum approach, which assumes that a discrete atomic structure can be replaced by an average constant atomic surface density of atoms that is assumed to be smeared over each molecule. We identify a circular hole in a graphene sheet as a nanopore and we consider the molecular interaction energy for both single-strand and double-strand DNA molecules assumed to move through the circular hole in a graphene sheet to determine the radius b of the hole that gives the minimum energy.

Modeling interactions between C₆₀ antiviral compounds and HIV protease.

Fullerenes have generated a great deal of interest in recent years, due to their properties and potential applications in many fields, including medicine. In this paper, we study an antiviral fullerene compound which may be used to treat the human immunodeficiency virus (HIV). We formulate a mathematical model which can describe the interaction energy between the C[Formula: see text] antiviral compounds and the HIV.

Offset configurations for single- and double-strand DNA inside single-walled carbon nanotubes.

Nanotechnology is a rapidly expanding research area, and it is believed that the unique properties of molecules at the nano-scale will prove to be of substantial benefit to mankind, especially so in medicine and electronics. Here we use applied mathematical modelling exploiting the basic principles of mechanics and the 6-12 Lennard-Jones potential function together with the continuum approximation, which assumes that intermolecular interactions can be approximated by average atomic surface densities. We consider the equilibrium offset positions for both single-strand and double-strand DNA molecules inside a single-walled carbon nanotube, and we predict offset positions with reference to the cross-section of the carbon nanotube.

High performance hydrogen storage from Be-BTB metal-organic framework at room temperature.

The metal-organic framework beryllium benzene tribenzoate (Be-BTB) has recently been reported to have one of the highest gravimetric hydrogen uptakes at room temperature. Storage at room temperature is one of the key requirements for the practical viability of hydrogen-powered vehicles. Be-BTB has an exceptional 298 K storage capacity of 2.

Methane storage in molecular nanostructures.

We survey various molecular structures which have been proposed as possible nanocontainers for methane storage. These are molecular structures that have been investigated through either experiments, molecular dynamics simulations or mathematical modelling. Computational simulation and mathematical modelling play an important role in predicting and verifying experimental outcomes, but both have their limitations.

Modelling peptide nanotubes for artificial ion channels.

We investigate the van der Waals interaction of D,L-Ala cyclopeptide nanotubes and various ions, ion-water clusters and C(60) fullerenes, using the Lennard-Jones potential and a continuum approach which assumes that the atoms are smeared over the peptide nanotube providing an average atomic density. Our results predict that Li(+), Na(+), Rb(+) and Cl(-) ions and ion-water clusters are accepted into peptide nanotubes of 8.5 Å internal diameter whereas the C(60) molecule is rejected.

Flow through a circular tube with a permeable Navier slip boundary.

For Newtonian fluid flow in a right circular tube, with a linear Navier slip boundary, we show that a second flow field arises which is different to conventional Poiseuille flow in the sense that the corresponding pressure is quadratic in its dependence on the length along the tube, rather than a linear dependence which applies for conventional Poiseuille flow. However, assuming that the quadratic pressure is determined, say from known experimental data, then the new solution only exists for a precisely prescribed permeability along the boundary. While this cannot occur for conventional pipe flow, for fluid flow through carbon nanotubes embedded in a porous matrix, it may well be an entirely realistic possibility, and could well explain some of the high flow rates which have been reported in the literature.

Instability of C₆₀ fullerene interacting with lipid bilayer.

Due to the large number of possible applications of nanoparticles in cosmetic and medical products, the possible hazards of nanoparticles in the human body are a major concern. A worst-case scenario is that nanoparticles might cause health issues such as skin damage or even induce cancer. As a first step to study the toxicity of nanoparticles, we investigate the energy behaviour of a C(60) fullerene interacting with a lipid bilayer.

The geometric structure of single-walled nanotubes.

In this paper, we survey a number of existing geometric structures which have been proposed by the authors as possible models for various nanotubes. Atoms assemble into molecules following the laws of quantum mechanics, and in general computational approaches to predicting the molecular structure can be arduous and involve considerable computing time. Fortunately, nature favours minimum energy structures which tend to be either very symmetric or very unsymmetric, and which therefore can be analyzed from a geometrical perspective.

Dislodgement of carbon nanotube bundles under pressure driven flow.

Experimental and predicted flow rates through carbon nanotubes vary considerably but generally are reported to be well in excess of that predicted by the conventional Poiseuille flow, and therefore nanotubes embedded in a matrix might provide membranes with exceptional mass transport properties. In this paper, applied mathematical modelling is undertaken to estimate the three forces acting on a nanotube bundle, namely the molecular interaction force, the viscous force, and the static pressure force. In deducing estimates of these forces we introduce a modification of the notion of the effective dead area for a carbon nanotube membrane, and we calculate the total forces necessary to push one or more of the nanotubes out of the bundle, thus creating a channel through which further enhancement of flow may take place.

Oscillation of carbon molecules inside carbon nanotube bundles.

In this paper, we investigate the mechanics of a nanoscaled gigahertz oscillator comprising a carbon molecule oscillating within the centre of a uniform concentric ring or bundle of carbon nanotubes. Two kinds of oscillating molecules are considered, which are a carbon nanotube and a C(60) fullerene. Using the Lennard-Jones potential and the continuum approach, we obtain a relation between the bundle radius and the radii of the nanotubes forming the bundle, as well as the optimum bundle size which gives rise to the maximum oscillatory frequency for both the nanotube-bundle and the C(60)-bundle oscillators.

An idealized polyhedral model and geometric structure for silicon nanotubes.

In this paper, we introduce an idealized model of silicon nanotubes comprising an exact polyhedral geometric structure for single-walled silicon nanotubes. The silicon nanotubes considered here are assumed to be formed by sp(3) hybridization and thus the nanotube lattice is assumed to comprise only squares or skew rhombi. Beginning with the three postulates that all bond lengths are equal, all adjacent bond angles are equal, and all atoms are equidistant from a common axis of symmetry, we derive exact formulae for the geometric parameters such as radii, bond angles and unit cell length.

Junctions between a boron nitride nanotube and a boron nitride sheet.

For future nanoelectromechanical signalling devices, it is vital to understand how to connect various nanostructures. Since boron nitride nanostructures are believed to be good electronic materials, in this paper we elucidate the classification of defect geometries for combining boron nitride structures. Specifically, we determine possible joining structures between a boron nitride nanotube and a flat sheet of hexagonal boron nitride.